What Is Standard Deviation? Plain-English Explanation with Examples

By Jorge Sanchez · April 20, 2026 · 6 min read

The average (mean) tells you the center of your data. But two datasets can have the same average while being completely different. Standard deviation measures the spread — how much individual values deviate from that average.

A Simple Example First

Two basketball players both average 20 points per game. But:

• Player A: 18, 21, 19, 22, 20 → Very consistent, low SD
• Player B: 35, 8, 40, 5, 12 → Very inconsistent, high SD

Standard deviation captures this difference. Player A has SD ≈ 1.6. Player B has SD ≈ 15.7.

How to Calculate Standard Deviation (Step by Step)

Using this sample dataset: 4, 8, 15, 16, 23, 42

1. Find the mean:
   Mean = (4+8+15+16+23+42) ÷ 6 = 108 ÷ 6 = 18
2. Subtract the mean from each value and square the result:

   Value	Value − Mean	(Value − Mean)²
   4	−14	196
   8	−10	100
   15	−3	9
   16	−2	4
   23	+5	25
   42	+24	576

3. Calculate variance:
   Population variance = (196+100+9+4+25+576) ÷ 6 = 910 ÷ 6 ≈ 151.7
   Sample variance = 910 ÷ (6−1) = 910 ÷ 5 = 182
4. Take the square root:
   Population SD = √151.7 ≈ 12.3
   Sample SD = √182 ≈ 13.5

Population SD vs. Sample SD

When do you divide by N vs. N−1?

• Population SD (÷ N): Use when your data IS the entire population. Example: all test scores in your class.
• Sample SD (÷ N−1): Use when your data is a sample from a larger population. Example: a survey of 100 people representing millions. Dividing by N−1 (Bessel's correction) gives a less biased estimate.

What Is a Good Standard Deviation?

There's no universal "good" SD — it depends on context:

• Low SD = data is consistent and clustered near the mean
• High SD = data is spread out and unpredictable
• For manufacturing (e.g., product dimensions), low SD = high quality
• For investment returns, SD is used to measure volatility/risk
• For test scores, a high SD means students performed very differently from each other

The 68-95-99.7 Rule (Normal Distribution)

For normally distributed data:

• 68% of values fall within ±1 SD of the mean
• 95% of values fall within ±2 SD of the mean
• 99.7% of values fall within ±3 SD of the mean

If IQ scores have a mean of 100 and SD of 15, then 95% of people have IQ between 70 and 130.